Biomedical Engineering Reference
In-Depth Information
mass transfer. The mass transfer of each of the components of air depends on the partial
pressure of each, as well as the metabolic load of the body, along with the diffusion distance
between alveoli and pulmonary capillaries. Oxygen is taken up by the bloodstream, and
carbon dioxide is given off to the lungs from the bloodstream. The exhaled gases are heated
to body temperature and are fully saturated with water vapor. Thus, when you place your
hand over your mouth as you exhale, the air feels warm and moist.
14.1.2 Membranes, Pores, and Diffusion
The gas exchange between the alveoli and the pulmonary capillaries is affected by the
partial pressures of each gas, the distance over which mass transfer occurs, and the surface
area for mass transfer. We can think of mass transfer as occurring across a membrane in a
steady-state fashion. This can be described by the one-dimensional, steady-state form of
Fick's Law:
Mass exchange rate
¼
DAdC
=
dx
where D is the
, A is the surface area for mass transfer, and dC/dx is the concen-
tration gradient for mass transfer.
For gases, the concentration gradient is the difference in the partial pressure. For a liquid or
for substances dissolved in a liquid (such as in blood or extracellular fluid), the concentration
gradient can be approximated by dC/dx, the difference in concentration over a specified
distance. The diffusivity (D) is a parameter that describes the relative ease by which a substance
moves throughout the “medium”—the fluid through which the substance moves. An example
of this is how sodium ions move through extracellular fluid. The diffusivity is thus affected by
both the medium and the substance to be transferred; it is a material property of both.
For gases, mass transfer occurs across the entire membrane, since gases are lipid soluble,
with membranes consisting of a layer of lipids and proteins. However, when the exchange
is of a liquid or a substance dissolved in a liquid (such as an ion), then the mass transfer
must occur through pores in the membrane. That is because most liquids are not lipid
soluble. When substances do indeed travel across pores, then there is selective mass transfer
due to the size of the pore as compared to the size of the substance that might transfer. This
selective mass transfer by means of the relative sizes is called
diffusivity
. Fick's Law is mod-
ified to account for such selective mass transfer by adding a permeability term (P), which
relates the area of the pores as compared to the total area of the membrane. At times, the
area for mass transfer (A) is instead described as A
P
rather than as the product of A
filtration
P.
An example of filtration is shown in Figure 14.7.
In general, the process by which mass transfer occurs via a concentration gradient is
called
. Diffusion is the macroscopic result of random thermal motion on a micro-
scopic scale. For example, in Figure 14.8, oxygen and nitrogen molecules move in random
directions, with kinetic energy on the order of kT, where k is the thermal conductivity
and T is the absolute temperature. If there are more oxygen molecules on the left side of
the plane A-A than on the right, more molecules will cross to the right than to the left; there
will be a net movement even though the motion of each individual molecule is completely
random. Diffusion in an open environment such as within extracellular fluid, and not con-
strained by a membrane for mass transfer, is shown in Figure 14.8.
diffusion
